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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE DGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T, 00002 $ BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT ) 00003 * 00004 * -- LAPACK test routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER LDA, LDB, LWORK, M, N, P 00010 * .. 00011 * .. Array Arguments .. 00012 DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), B( LDB, * ), 00013 $ BF( LDB, * ), BWK( LDB, * ), Q( LDA, * ), 00014 $ R( LDA, * ), RESULT( 4 ), RWORK( * ), 00015 $ T( LDB, * ), TAUA( * ), TAUB( * ), 00016 $ WORK( LWORK ), Z( LDB, * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * DGQRTS tests DGGQRF, which computes the GQR factorization of an 00023 * N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z. 00024 * 00025 * Arguments 00026 * ========= 00027 * 00028 * N (input) INTEGER 00029 * The number of rows of the matrices A and B. N >= 0. 00030 * 00031 * M (input) INTEGER 00032 * The number of columns of the matrix A. M >= 0. 00033 * 00034 * P (input) INTEGER 00035 * The number of columns of the matrix B. P >= 0. 00036 * 00037 * A (input) DOUBLE PRECISION array, dimension (LDA,M) 00038 * The N-by-M matrix A. 00039 * 00040 * AF (output) DOUBLE PRECISION array, dimension (LDA,N) 00041 * Details of the GQR factorization of A and B, as returned 00042 * by DGGQRF, see SGGQRF for further details. 00043 * 00044 * Q (output) DOUBLE PRECISION array, dimension (LDA,N) 00045 * The M-by-M orthogonal matrix Q. 00046 * 00047 * R (workspace) DOUBLE PRECISION array, dimension (LDA,MAX(M,N)) 00048 * 00049 * LDA (input) INTEGER 00050 * The leading dimension of the arrays A, AF, R and Q. 00051 * LDA >= max(M,N). 00052 * 00053 * TAUA (output) DOUBLE PRECISION array, dimension (min(M,N)) 00054 * The scalar factors of the elementary reflectors, as returned 00055 * by DGGQRF. 00056 * 00057 * B (input) DOUBLE PRECISION array, dimension (LDB,P) 00058 * On entry, the N-by-P matrix A. 00059 * 00060 * BF (output) DOUBLE PRECISION array, dimension (LDB,N) 00061 * Details of the GQR factorization of A and B, as returned 00062 * by DGGQRF, see SGGQRF for further details. 00063 * 00064 * Z (output) DOUBLE PRECISION array, dimension (LDB,P) 00065 * The P-by-P orthogonal matrix Z. 00066 * 00067 * T (workspace) DOUBLE PRECISION array, dimension (LDB,max(P,N)) 00068 * 00069 * BWK (workspace) DOUBLE PRECISION array, dimension (LDB,N) 00070 * 00071 * LDB (input) INTEGER 00072 * The leading dimension of the arrays B, BF, Z and T. 00073 * LDB >= max(P,N). 00074 * 00075 * TAUB (output) DOUBLE PRECISION array, dimension (min(P,N)) 00076 * The scalar factors of the elementary reflectors, as returned 00077 * by DGGRQF. 00078 * 00079 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) 00080 * 00081 * LWORK (input) INTEGER 00082 * The dimension of the array WORK, LWORK >= max(N,M,P)**2. 00083 * 00084 * RWORK (workspace) DOUBLE PRECISION array, dimension (max(N,M,P)) 00085 * 00086 * RESULT (output) DOUBLE PRECISION array, dimension (4) 00087 * The test ratios: 00088 * RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP) 00089 * RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP) 00090 * RESULT(3) = norm( I - Q'*Q ) / ( M*ULP ) 00091 * RESULT(4) = norm( I - Z'*Z ) / ( P*ULP ) 00092 * 00093 * ===================================================================== 00094 * 00095 * .. Parameters .. 00096 DOUBLE PRECISION ZERO, ONE 00097 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00098 DOUBLE PRECISION ROGUE 00099 PARAMETER ( ROGUE = -1.0D+10 ) 00100 * .. 00101 * .. Local Scalars .. 00102 INTEGER INFO 00103 DOUBLE PRECISION ANORM, BNORM, RESID, ULP, UNFL 00104 * .. 00105 * .. External Functions .. 00106 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY 00107 EXTERNAL DLAMCH, DLANGE, DLANSY 00108 * .. 00109 * .. External Subroutines .. 00110 EXTERNAL DGEMM, DGGQRF, DLACPY, DLASET, DORGQR, DORGRQ, 00111 $ DSYRK 00112 * .. 00113 * .. Intrinsic Functions .. 00114 INTRINSIC DBLE, MAX, MIN 00115 * .. 00116 * .. Executable Statements .. 00117 * 00118 ULP = DLAMCH( 'Precision' ) 00119 UNFL = DLAMCH( 'Safe minimum' ) 00120 * 00121 * Copy the matrix A to the array AF. 00122 * 00123 CALL DLACPY( 'Full', N, M, A, LDA, AF, LDA ) 00124 CALL DLACPY( 'Full', N, P, B, LDB, BF, LDB ) 00125 * 00126 ANORM = MAX( DLANGE( '1', N, M, A, LDA, RWORK ), UNFL ) 00127 BNORM = MAX( DLANGE( '1', N, P, B, LDB, RWORK ), UNFL ) 00128 * 00129 * Factorize the matrices A and B in the arrays AF and BF. 00130 * 00131 CALL DGGQRF( N, M, P, AF, LDA, TAUA, BF, LDB, TAUB, WORK, LWORK, 00132 $ INFO ) 00133 * 00134 * Generate the N-by-N matrix Q 00135 * 00136 CALL DLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) 00137 CALL DLACPY( 'Lower', N-1, M, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) 00138 CALL DORGQR( N, N, MIN( N, M ), Q, LDA, TAUA, WORK, LWORK, INFO ) 00139 * 00140 * Generate the P-by-P matrix Z 00141 * 00142 CALL DLASET( 'Full', P, P, ROGUE, ROGUE, Z, LDB ) 00143 IF( N.LE.P ) THEN 00144 IF( N.GT.0 .AND. N.LT.P ) 00145 $ CALL DLACPY( 'Full', N, P-N, BF, LDB, Z( P-N+1, 1 ), LDB ) 00146 IF( N.GT.1 ) 00147 $ CALL DLACPY( 'Lower', N-1, N-1, BF( 2, P-N+1 ), LDB, 00148 $ Z( P-N+2, P-N+1 ), LDB ) 00149 ELSE 00150 IF( P.GT.1 ) 00151 $ CALL DLACPY( 'Lower', P-1, P-1, BF( N-P+2, 1 ), LDB, 00152 $ Z( 2, 1 ), LDB ) 00153 END IF 00154 CALL DORGRQ( P, P, MIN( N, P ), Z, LDB, TAUB, WORK, LWORK, INFO ) 00155 * 00156 * Copy R 00157 * 00158 CALL DLASET( 'Full', N, M, ZERO, ZERO, R, LDA ) 00159 CALL DLACPY( 'Upper', N, M, AF, LDA, R, LDA ) 00160 * 00161 * Copy T 00162 * 00163 CALL DLASET( 'Full', N, P, ZERO, ZERO, T, LDB ) 00164 IF( N.LE.P ) THEN 00165 CALL DLACPY( 'Upper', N, N, BF( 1, P-N+1 ), LDB, T( 1, P-N+1 ), 00166 $ LDB ) 00167 ELSE 00168 CALL DLACPY( 'Full', N-P, P, BF, LDB, T, LDB ) 00169 CALL DLACPY( 'Upper', P, P, BF( N-P+1, 1 ), LDB, T( N-P+1, 1 ), 00170 $ LDB ) 00171 END IF 00172 * 00173 * Compute R - Q'*A 00174 * 00175 CALL DGEMM( 'Transpose', 'No transpose', N, M, N, -ONE, Q, LDA, A, 00176 $ LDA, ONE, R, LDA ) 00177 * 00178 * Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) . 00179 * 00180 RESID = DLANGE( '1', N, M, R, LDA, RWORK ) 00181 IF( ANORM.GT.ZERO ) THEN 00182 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) / 00183 $ ULP 00184 ELSE 00185 RESULT( 1 ) = ZERO 00186 END IF 00187 * 00188 * Compute T*Z - Q'*B 00189 * 00190 CALL DGEMM( 'No Transpose', 'No transpose', N, P, P, ONE, T, LDB, 00191 $ Z, LDB, ZERO, BWK, LDB ) 00192 CALL DGEMM( 'Transpose', 'No transpose', N, P, N, -ONE, Q, LDA, B, 00193 $ LDB, ONE, BWK, LDB ) 00194 * 00195 * Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) . 00196 * 00197 RESID = DLANGE( '1', N, P, BWK, LDB, RWORK ) 00198 IF( BNORM.GT.ZERO ) THEN 00199 RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, N ) ) ) / BNORM ) / 00200 $ ULP 00201 ELSE 00202 RESULT( 2 ) = ZERO 00203 END IF 00204 * 00205 * Compute I - Q'*Q 00206 * 00207 CALL DLASET( 'Full', N, N, ZERO, ONE, R, LDA ) 00208 CALL DSYRK( 'Upper', 'Transpose', N, N, -ONE, Q, LDA, ONE, R, 00209 $ LDA ) 00210 * 00211 * Compute norm( I - Q'*Q ) / ( N * ULP ) . 00212 * 00213 RESID = DLANSY( '1', 'Upper', N, R, LDA, RWORK ) 00214 RESULT( 3 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP 00215 * 00216 * Compute I - Z'*Z 00217 * 00218 CALL DLASET( 'Full', P, P, ZERO, ONE, T, LDB ) 00219 CALL DSYRK( 'Upper', 'Transpose', P, P, -ONE, Z, LDB, ONE, T, 00220 $ LDB ) 00221 * 00222 * Compute norm( I - Z'*Z ) / ( P*ULP ) . 00223 * 00224 RESID = DLANSY( '1', 'Upper', P, T, LDB, RWORK ) 00225 RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP 00226 * 00227 RETURN 00228 * 00229 * End of DGQRTS 00230 * 00231 END
1.7.3 
